1. Field of the Invention
The present invention relates to a method and apparatus for pulse shaping output of a digital modulator.
2. Description of the Relate Art
Digital communication relies on numerous different, albeit related, forms of digital modulation such as phase shift keying (PSK), bi-phase shift keying (BPSK), quadrature phase shift keying (QPSK or 4-PSK), and quadrature amplitude modulation (QAM).
BPSK will be described with reference to FIG. 1. As shown, the magnitude of a reference carrier is constant, and to transmit either a 0 or a 1, the phase thereof is xe2x80x9ckeyedxe2x80x9d or switched between 0xc2x0 and 180xc2x0. A receiver then decides whether a 0 or a 1 was transmitted based on the phase of the received carrier, and generates the original data stream. With this simple scheme, one bit of information is transmitted with each state or symbol, so that the carrier phase is keyed at the data rate. FIG. 1 also illustrates the constellation for BPSK. As shown, the BPSK constellation diagram includes two points in the I-Q plane where I stands for in-phase (i.e., phase reference) and Q stands for quadrature (i.e., 90xc2x0 out-of-phase). The two points in the BPSK constellation diagram represent the position of the signal at the xe2x80x9ctiming instancexe2x80x9d. The timing instance is when the receiver interprets the signal. The signal can only be at one position at a time, but the constellation can be thought of as having persistence so that all proper states appear. Constellation diagrams such as in FIG. 1 typically do not show the transition between states and it should be noted that this transition does take a finite time. But for clarity, the transitions are not shown otherwise traces connecting the two states would clutter the diagram.
FIG. 2 illustrates the constellation diagram for QPSK. As shown, four different states exist in the QPSK diagram at phase values of 45xc2x0, 135xc2x0, 225xc2x0, and 315xc2x0. As further shown, each state corresponds to a symbol representing two bits. Because the data is taken two bits at a time to form a symbol, the symbol rate is half the bit rate. As a result, QPSK requires half the band width of BPSK for the same bit rate.
As a further example, FIG. 3 illustrates the constellation for 16 QAM. According to this modulation format, four bits of serial data are encoded as a single phase state or symbol. In order to generate this type of modulation, the I and Q carriers need to take four different possible levels of amplitude, typically +3, +1, xe2x88x921, xe2x88x923, depending on the code being transmitted. In 16 QAM, four bits of serial data are transmitted with each symbol.
By passing these modulation schemes immediately through a bandlimited channel, the pulses will spread in time, and the pulse for each symbol will smear into time intervals of succeeding symbols. This causes intersymbol interference and leads to an increased probability of the receiver making an error in detecting a symbol. Lowering this undesired effect by increasing bandwidth is not possible in many applications such as wireless communication systems because these applications operate with minimal bandwidth. Thus, techniques that reduce the bandwidth and suppress out-of-band radiation, while reducing intersymbol interference, are highly desirable.
Therefore, pulse shaping plays a crucial role in making digitally modulated data recognizable during filtering of the digitally modulated data to an acceptable bandwidth. The term data as used in this application refers to the modulation output, and not what that modulation output represents (e.g., audio information).
A typical pulse shaping operation performs the following function:                                                         p              l                        ⁡                          (              k              )                                =                                                                      ∑                                      M                    -                    1                                                                    m                  =                  0                                            ⁢                                                s                  ⁡                                      (                                          k                      -                      m                                        )                                                  ⁢                                  c                  ⁡                                      (                                          Lm                      +                      l                                        )                                                  ⁢                                  xe2x80x83                                ⁢                for                ⁢                                  xe2x80x83                                ⁢                l                                      =            0                          ,        1        ,        …        ⁢                  xe2x80x83                ,                  L          -          1                                    (        1        )            
where s(kxe2x88x92m) represents the symbol output from the digital modulation operation to be transmitted; c(Lm+1) represents a filter coefficient; L represent the total number of phases or cycles in the digital modulation (not the phase of a symbol); M represents the total number of coefficients at each phase, which depends on the level of filtering being performed; and 1 represents the current phase. The symbols s(k) are generated by the digital modulation operation, and the total number of phases L, the coefficients c(k), and the total number of coefficients M at each phase are predetermined based on the format of the digital modulation and the type of filtering being performed.
As evidenced by equation (1), the pulse shaping operation requires many multiplication and addition operations. In, for example, a modem transceiver, the pulse shaping operation consumes a large portion of the modem""s overall computational power. Accordingly, a need exists for a greatly simplified method of pulse shaping which does not consume large amounts of computational power; namely, performs relatively few mathematical operations.
The method of pulse shaping and the pulse shaper according to the present invention significantly reduce the amount of computation required to perform the pulse shaping operation by reducing the pulse shaping operation to simple add or subtract arithmetic operations. The inventors of the present invention recognized the following two attributes of each set of bits representing a symbol: (1) one of the bits indicates whether the coefficient corresponding to that set of bits for forming a pulse shaped value should be added or subtracted, and (2) another bit in the set of bits indicates whether the coefficient being added or subtracted should be added or subtracted to form a real or imaginary output value of the pulse shaping operation. Therefore, pulse shaped values can be generated according to the present invention by adding or subtracting a received coefficient to or from a received value based on the bit in the set of bits indicating whether addition or subtraction should take place, and then selectively supplying the output thereof as either a real or imaginary result based on the other bit in the set of bits indicating whether the generated value represents a real or imaginary value.